Eviction-like resonances for satellite orbits. Application to Phobos, the main satellite of Mars

TL;DR

This paper investigates secular eviction-like resonances affecting satellite orbits, focusing on Phobos, and analyzes how these resonances can alter orbital parameters, potentially causing chaotic motion and orbital instability.

Contribution

It provides a detailed analysis of eviction-like secular resonances, their impact on satellite orbits, and the conditions for resonance capture, especially applied to Phobos.

Findings

Resonance crossing can significantly alter satellite inclination.

Capture into resonance occurs mainly during decreasing semi-major axis.

Overlapping resonances can lead to chaotic orbital behavior.

Abstract

The motion of a satellite can experience secular resonances between the precession frequencies of its orbit and the mean motion of the host planet around the star. Some of these resonances can significantly modify the eccentricity (evection resonance) and the inclination (eviction resonance) of the satellite. In this paper, we study in detail the secular resonances that can disturb the orbit of a satellite, in particular the eviction-like ones. Although the inclination is always disturbed while crossing one eviction-like resonance, capture can only occur when the semi-major axis is decreasing. This is, for instance, the case of Phobos, the largest satellite of Mars, that will cross some of these resonances in the future because its orbit is shrinking owing to tidal effects. We estimate the impact of resonance crossing in the orbit of the satellite, including the capture probabilities, as a function of several parameters, such as the eccentricity and the inclination of the satellite, and the obliquity of the planet. Finally, we use the method of the frequency map analysis to study the resonant dynamics based on stability maps, and we show that some of the secular resonances may overlap, which leads to chaotic motion for the inclination of the satellite.